From your post, I get the impression you are not familiar with the cycling process? It is important that you understand the process and how it will affect your axolotl as spikes in ammonia and nitrite that occur during the cycling process can cause harm to aquatic life.
In a nutshell, aquatic life such as axolotls produce waste that turns into ammonia. a type of bacteria starts feeding on the ammonia and convert the ammonia into nitrite. Then, a different type of bacteria feeds on the nitrite and converts the nitrite into nitrate. So in an uncycled tank, there are no established colonies of the ammonia/nitrite eating bacteria. The purpose of cycling a tank is to establish colonies of bacteria so that the aquatic life are not exposed to dangerous levels of ammonia and nitrite. Nitrate is the end part of the cycle and whilst it does not pose the same toxin risks as ammonia and nitrite, it is still toxic in high levels and so we need to maintain nitrate within a safe level by removing the nitrate through regular water changes. A cycled tank will read zero ammonia, zero nitrite and a reading of nitrate. You want to keep nitrate below 40ppm.
Here is a link on cycling. Hopefully it will help.
Scales Tails Wings and Things, What is Aquarium Cycling? How to Cycle your Tank
It takes weeks to cycle a tank so if you have not already cycled your tank, it will not be cycled before your axolotl arrives. You will need to decide whether you do a fishless cycle or cycle the tank with the axolotl in the tank. With the axolotl in the tank, you would need to conduct frequent water changes to ensure the levels of ammonia and nitrite remain at safe levels (below 0.25ppm). With a fishless cycle, you would need an alternative place to keep your axolotl until the tank is fully cycled. Keeping the axolotl in a tub of cool, clean, dechlorinated water and doing daily 100% water changes is needed. You could have a second tub pre-prepared next to the first tub so you can transfer the axolotl each day and pour the old water into the tank to help the cycling process. Whilst doing the fishless cycle, you would need an ammonia source such as pure ammonia to feed the bacteria.
Personally, I would do the fishless cycling method. I believe it is safer for your axolotl and the process is easier and can be a little quicker (although it still takes weeks). If you can source some material from an already cycled tank, such as filter media, this will help speed up the process. Below is a link to a guide on how to do a fishless cycle.
The (almost) Complete Guide and FAQ to Fishless Cycling - Aquarium Advice - Aquarium Forum Community